PD555, Read the FAQ and Help accurizing links, you can rest assured that you haven't experienced anything that's new, shooting a single shot break barrel requires some techniques that may be new to you compared to a bolt gun with one piece stock.
The transfer bar requires a full pull to the rear to keep it in the firing position, letting off the trigger at the break will cause inconsistent pin strikes and accuracy will be poor due to it.
It may not like the ammo either, I wouldn't assume just because you're using premium ammo that it's gonna shoot one hole groups, most NEF/H&Rs shoot standard ammo very well, the Rem Cor-lokts and Federal Fusion ammo seem to be consistently good shooters across the spectrum of calibers.
As Fazak said, cleaning good from the get go is important, and taking it a step further and doing a good bore polishing with a fine metal polish like JB or Flitz as mentioned in the FAQ, will reduce range time considerably, I do all of mine before I even shoot em, I don't have a poor shooter in the bunch in over 25 rifles.
Also, just because the scope is new doesn't give it a free pass, there have been many NIB scope problems reported here in the past, don't rule it out. I just had a problem with a brand spanking new Nikon Buckmasters, so it happens.
Also, make sure the latch and latch shelf are oil free, storing a rifle muzzle up allows oil from the bore and barrel to run down into the frame resulting in an oily latch shelf which can impact accuracy big time, it's the number one reason for firearms returned to H&R for accuracy problems. Some shooters report that oiling the latch can improve accuracy, but the majority shoot well dry, and that's been my experience so far. I tried the oily latch on my last range visit, didn't work on 2 different rifles.
And if all else fails, give H&R a call and make arrangements on their dime to have it fixed, their CS is second to none!
Hang in there, we're here to help, you aren't the first and not the last to have an accuracy problem.
Tim
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